Use of Secondary Data to Estimate Instantaneous Model Parameters of Diabetic Heart Disease: Lemonade Method

With the increasing burden of chronic diseases on the health care system, Markov-type models are becoming popular to predict the long-term outcomes of early intervention and to guide disease management. However, statisticians have not been actively involved in the development of these models. Typically, the models are developed by using secondary data analysis to find a single "best" study to estimate each transition in the model. However, due to the nature of secondary data analysis, there frequently are discrepancies between the theoretical model and the design of the studies being used. This paper illustrates a likelihood approach to correctly model the design of clinical studies under the conditions where 1) the theoretical model may include an instantaneous state of distinct interest to the researchers, and 2) the study design may be such that study data can not be used to estimate a single parameter in the theoretical model of interest. For example, a study may ignore intermediary stages of disease. Using our approach, not only can we accommodate the two conditions above, but more than one study may be used to estimate model parameters. In the spirit of "If life gives you lemon, make lemonade", we call this method "Lemonade Method". Simulation studies are carried out to evaluate the finite sample property of this method. In addition, the method is demonstrated through application to a model of heart disease in diabetes.